Question

The angles of a triangle are (x + 21)°, x° and (2x – 45)°. Find the measure of these angles.

Answer 1

$\rm{(x+21)^\circ+(2x-45)^\circ+x^\circ=180^\circ\quad...\:Angle\:Sum\:Property\:In\:Triangle}$

$\longrightarrow\rm{x+21^\circ+2x-45^\circ+x=180^\circ}$

$\longrightarrow\rm{x+2x+x+21^\circ-45^\circ=180^\circ}$

$\longrightarrow\rm{4x-24^\circ=180^\circ}\longrightarrow\rm{4x-24^\circ+24^\circ=180^\circ+24^\circ}$

$\longrightarrow\rm{4x=204^\circ}\longrightarrow\rm{x=204^\circ/4=51^\circ}$

$\rm{\bigstar\:\:Now\:The\:Angles\:Are\:;}$

$\longrightarrow\rm{x=204^\circ/4=51^\circ}$

$\longrightarrow\rm{(x+21)^\circ=51^\circ+21^\circ=72^\circ}$

$\longrightarrow\rm{(2x-45)^\circ=2(51^\circ)-45^\circ=102^\circ-45^\circ=57^\circ}$